Measuring missing heritability: inferring the contribution of common variants

Abstract

Genome-wide association studies (GWASs), also called common variant association studies (CVASs), have uncovered thousands of genetic variants associated with hundreds of diseases. However, the variants that reach statistical significance typically explain only a small fraction of the heritability. One explanation for the "missing heritability" is that there are many additional disease-associated common variants whose effects are too small to detect with current sample sizes. It therefore is useful to have methods to quantify the heritability due to common variation, without having to identify all causal variants. Recent studies applied restricted maximum likelihood (REML) estimation to case-control studies for diseases. Here, we show that REML considerably underestimates the fraction of heritability due to common variation in this setting. The degree of underestimation increases with the rarity of disease, the heritability of the disease, and the size of the sample. Instead, we develop a general framework for heritability estimation, called phenotype correlation-genotype correlation (PCGC) regression, which generalizes the well-known Haseman-Elston regression method. We show that PCGC regression yields unbiased estimates. Applying PCGC regression to six diseases, we estimate the proportion of the phenotypic variance due to common variants to range from 25% to 56% and the proportion of heritability due to common variants from 41% to 68% (mean 60%). These results suggest that common variants may explain at least half the heritability for many diseases. PCGC regression also is readily applicable to other settings, including analyzing extreme-phenotype studies and adjusting for covariates such as sex, age, and population structure.

Keywords: genome-wide association studies; heritability estimation; statistical genetics.

Fig. 1.

Distributions of genetic effects, environmental effects, phenotypes, and liabilities in three study designs. In each of A, B, and C, a phenotype is assumed to depend on the sum of a genetic effect and an environmental effect. The scatterplot shows the joint distribution of the genetic and environmental effects, the upper left shows the marginal distributions of the environmental effect, the upper right shows the marginal distributions of the genetic effect, and the lower portion shows the marginal distribution of the phenotype. (A) Quantitative phenotype in a random sample of the population. (B) Disease phenotype in a random sample of the population. (C) Disease trait in a balanced case–control study. Disease phenotypes were simulated under a liability threshold model with disease prevalence of 10% (B) and 0.1% (C), with red points indicating affected individuals (liability above the threshold) and black points indicating unaffected individuals (liability below the threshold). In C, the marginal distributions of the genetic and environmental effects no longer are normally distributed, and there is an induced positive correlation between the genetic and environmental effects (r = 0.53).

Fig. 2.

Comparison of REML and PCGC regression. (A) REML yields biased estimates for case–control studies of diseases, whereas PCGC regression yields unbiased estimates. We simulated case–control studies for nine combinations of K (prevalence) and P (proportion of cases among overall samples), and for five values of h² (0.1, 0.3, 0.5, 0.7, and 0.9). For each combination of parameters, we show the average of 10 heritability estimates obtained by applying the REML method of Lee et al. (10) and PCGC regression to our simulated case–control data. REML produced biased estimates, whereas PCGC regression produced unbiased estimates for all scenarios. The bias of REML estimates increases as both the true heritability and overrepresentation of cases increase. To demonstrate the severity of the bias, consider the scenario of a disease with prevalence of 0.1% in a balanced case–control study (values typical for Crohn's disease or MS). When the true heritability is 50%, the estimated heritability would be 30% on average, as indicated by the black dots. (B) Heritability estimates for case–control studies with increasing sample size. Simulated case–control studies are as previously described, with the prevalence of the disease, the proportion of cases, and the heritability fixed at 1%, 30%, and 50%, respectively. The size of simulated studies ranged from 2,000 to 8,000. The bias of heritability estimates from REML increases with study size, whereas those from PCGC regression estimates remain unbiased. (C) Heritability estimation in the presence of fixed effects. We simulated case–control studies with an additional “sex” covariate, which either has no effect on the disease or increases the relative risk (RR) by twofold or fourfold. The prevalence of the disease in the population was 0.5%, the heritability was set to 50%, and the numbers of cases and controls were equal. Applying REML with or without accounting for the additional covariate resulted in underestimation of the heritability. Moreover, inclusion of the covariate as a fixed effect resulted in even lower estimates of heritability when the effect of the covariate on the phenotype was considerable. By contrast, PCGC regression correctly accounted for the presence of the covariate.